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- Question
- If an integer is selected at random from 1 to 100. The probability that it relatively prime to 100 is?
Options- A. 2/5
- B. 61/100
- C. 17/100
- D. 19/100
- Correct Answer
- 2/5
ExplanationFrom the set of odd number < 100, if we exclude multiples of 5, we get the set of numbers < 100 and relatively prime to 100.
The number of such numbers = 50 - 10 = 40
? Reqd. Probability = 40 / 100 = 2/5 - 1. The number of tosses that have to be made in order that there is 99% probability of getting at least one head is?
Options- A. 5
- B. 7
- C. 6
- D. 8 Discuss
- 2. The probability that a marksman will hit a target is given as 1/5. Then his probability of at least one hit in 10 shots, is?
Options- A. 1 - (4/5)10
- B. 1/ (5)10
- C. 1 - 1/ (5)10
- D. (4/5)10 Discuss
- 3. The probability that a person will hit a target in shooting practice is 0.3 . If he shoots 10 times. Then the probability of his shooting the target is?
Options- A. 1
- B. 1 - (0.7)10
- C. (0.7)10
- D. (0.3)10 Discuss
- 4. The probability that a man lives after 10 years is 1/4 and that his wife is alive after 10 years is 1/3. The probability that neither of them is alive after 10 years is?
Options- A. 1/2
- B. 1/12
- C. 7/12
- D. 3/4 Discuss
- 5. The chance of throwing a total of 3 or 5 or 11 with two dics is?
Options- A. 5/36
- B. 1/9
- C. 2/9
- D. 19/36 Discuss
- 6. n books are to be arranged on a self. These include m volumes of a science book (m < n). The probability that in any arrangement, the volumes of science books are in ascending order is?
Options- A. 1/ n!
- B. 1/n-m!
- C. 1/m!
- D. m!/n! Discuss
- 7. The probability that a man aged x years will die in a years is p. The probability that out of n men M1, M2, M3...... Mn each aged n years Mk will die and be the first to die is?
Options- A. 1/n2
- B. 1 - (1 - p)n
- C. 1/n2[1 - (1- p)n
- D. 1/n[1 - (1 - p)n] Discuss
- 8. If the probability of machine failing during a day is 0.95. The probability of its working for four consecutive days without failing is?
Options- A. 0.00000625
- B. 0.0625
- C. 0.16548375
- D. 0.000625 Discuss
- 9. Seven white balls and three black ball are randomly placed in a row. The probability that no two black balls are placed adjacently equals?
Options- A. 1/2
- B. 7/15
- C. 2/15
- D. 1/3 Discuss
- 10. The probability of occurrence of a multiple of 2 on a dice and multiple of 3 on the other dice . If both are thrown together is?
Options- A. 7/26
- B. 1/3
- C. 71/36
- D. 1/4 Discuss
Probability problems
Search Results
Correct Answer: 7
Explanation:
Corresponding to n tosses, the Probability of getting no head = (1/2)n and,
Therefore, the probability of getting at least one head = 1 - (1/2)n
Now, 1 - (1/2)n ? 99/100
? (1/2)n ? 1/100
? n ? 7
Correct Answer: 1 - (4/5)10
Explanation:
? p = 1/5
? q = 1 - 1/5 = 4/5
The probability that none will hit in 10 shots = (4/5)10
? Reqd. probability = 1 - (4/5)10
Correct Answer: (0.3)10
Explanation:
? Probability in each trial (shooting) = 0.3
? Reqd. probability = (0.3)10
Correct Answer: 1/2
Explanation:
P(M) = 1/4; P(W)= 1/3
? P (M) = 1 - 1/4 = 3/4
? P(W)= 1 - 1/3 = 2/3
Reqd. probability = P(M) P(W) = 3/4 x 2/3 = 1/2
Correct Answer: 2/9
Explanation:
? Probability for 3 = (1, 2), (2, 1) = 2/36
? Probability for 5 = (1, 4), (2, 3), (3, 2), (4, 1)= 4/ 36
? Probability for 11 (5, 6), (6, 5) = 2/36
? Reqd . Probability = 2/36 + 4/36 + 2/36 = 8/36 = 2/9
Correct Answer: 1/m!
Explanation:
Corresponding to each arrangement of (n - m) other books, there is a unique arrangement of the m volumes of the science book in ascending order and m! arrangement of the m volumes in random order
&Reqd. Prob = p = 1/m!
Correct Answer: 1/n[1 - (1 - p)n]
Explanation:
? Probability that no man out of n men aged x years will die in a year = (1 - p)n
? Probability that out of n men at least one will die in a year = 1 - (1 - p)n .
When at least one, man dies, any one out of the n men may be the first to die
Correct Answer: 0.0625
Explanation:
? Probability of machine failing during a day p = 0.95
? q = Probability of its working during a day = 1 - p = 1 - 0.95 = 0.05
Required probability = q4 = (0.05)4
= 0.00000625
Correct Answer: 7/15
Explanation:
n(S) = 10C7 = 10C3
n(E) = 8C3
? P(E) = n(E)/n(S) = 7/15
Correct Answer: 1/3
Explanation:
Probability of multiple of 2 = 3/6 = 1/2
Probability of multiple of 3 = 2/6 = 1/3
Since there are two dice.
? The required probability = 2 x 1/2 x 1/3 = 1/3
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